Since $b = 0 + i$ is a nonreal complex number we know that $2^i$ takes on infinitely many values that differ by a multiple of $e^{2kb\pi i} = e^{2k\pi i^2} = e^{-2k\pi}$, $k \in \mathbb{Z}$. Therefore all possible values for $2^i$ are given for $k \in \mathbb{Z}$ by: